Using an approach similar to Roy’s safety-first risk rule (Econometrica 1952), the authors randomly generate portfolios using the S&P 500 Index as the universe of available stocks. To test investment management skill, the randomly generated portfolios are compared with a large sample of professionally managed portfolios consisting of US long-only large-cap stocks. Although the results are consistent with those of previous findings (i.e., that markets are efficient), the authors use an innovative approach to conducting their experiment. They use a probability-based analysis and explore the implications of such an approach.

This research is useful to practitioners who invest in long-only equity portfolios with a turnover ratio of around 100%. The turnover ratio of 100% is represented by one of the assumptions in the analysis, which stipulates that each randomly generated portfolio be sold at each year-end and then randomly repurchased at the beginning of the year.

For the universe and investment horizon tested, the results indicate that a naive beta strategy (i.e., a randomly generated portfolio) is probabilistically geared to perform as well as a consciously managed portfolio. Some outperformance of the markets is expected because the portfolios are not risk adjusted. Neither the random portfolios nor the managed portfolios follow a particular pattern of performance. The more concentrated random portfolios tend to outperform in years other than times of crisis or bear market rallies. The tech bubble benefited managed portfolios and weakened the results of the more diversified random portfolios. The authors suggest that asset managers may lack tools that have predictive power or may be constrained by mandates, although they do tend to outperform during bull markets.

The focus of previous studies of actively managed portfolios has generally been on the efficiency of the markets (comparing actively managed portfolios with passive portfolios). To reflect strategies used in extreme times, a more recent study compared three portfolio strategies (random, index benchmark, and smart beta) with the markets by using the actual returns of professional managers. In addition, an attempt has been made to measure the determinants of skill or luck. The authors of this research consider whether it is either skill or luck that determines performance.

For the investment period from 1 January 1991 to the end of 2011, the authors randomly select stocks from each year to construct their test portfolios. To avoid selection bias, the authors use Mercer’s Global Investment Manager Database (GIMD) in choosing the actively managed accounts. A sample size of 10,000 randomly generated portfolios is chosen to allow for a more accurate inference of probability density functions while avoiding selection bias. The proportion of each stock in the portfolio is also random but must be greater than 0% and less than 100%. A portfolio of 30 stocks is chosen because the marginal benefits of diversification are found to become nil beyond 30; a portfolio of 3 stocks is chosen to demonstrate the idiosyncratic effects, and a portfolio of 100 stocks is chosen to demonstrate the full benefits of diversification while being less than the investment universe of 500 stocks.

To follow the reality of the market over the 20-year time period of the study, the portfolios are turned over annually. To study the effects of various economic cycles, the authors use the Akaike information criterion to assign cross-sectional probability density functions that best describe the performance of both random and managed portfolios. They state that a significant number of the inferred distributions are nonnormal.

The authors conclude that randomly selected portfolios perform just as well as actively managed portfolios. But these results are limited by the assumptions they make. The authors do note that the results cannot necessarily be extrapolated to asset managers in general and are only representative of the asset managers in the sample. It is unclear whether the assumptions used to create the random portfolios fairly represent the characteristics inherent to managed portfolios, which may have different holding periods, and whether the universe of managed portfolios is limited to that of the S&P 500.